{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:I26VAXQVXTV6NV5VEH7TTTML4A","short_pith_number":"pith:I26VAXQV","schema_version":"1.0","canonical_sha256":"46bd505e15bcebe6d7b521ff39cd8be017a8374bdc05a08dd91161895b6a447f","source":{"kind":"arxiv","id":"1311.6025","version":1},"attestation_state":"computed","paper":{"title":"Weighted norm inequalities for fractional maximal operators--a Bellman function approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.CA","authors_text":"Adam Osekowski, Rodrigo Banuelos","submitted_at":"2013-11-23T17:34:33Z","abstract_excerpt":"We study classical weighted $L^p\\to L^q$ inequalities for the fractional maximal operators on $\\R^d$, proved originally by Muckenhoupt and Wheeden in the 70's. We establish a slightly stronger version of this inequality with the use of a novel extension of Bellman function method.\n  More precisely, the estimate is deduced from the existence of a certain special function which enjoys appropriate majorization and concavity. From this result and an explicit version of the ``$A_{p-\\varepsilon}$ theorem,\" derived also with Bellman functions, we obtain the sharp inequality of Lacey, Moen, P\\'erez an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1311.6025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-23T17:34:33Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"9b7a71155bbf2a049574fd6976707518ece02f5b6363ec68c3f867267846a1bc","abstract_canon_sha256":"02e47f5b0d4cd84888e2ccb7ba8214fdc7c7c6dccd72d8c7b10dcc4334e9f065"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:20.814671Z","signature_b64":"d+wEUNiHx/WfNwfsXW1jeSe0tLUtRmoJIVsxzjg0uORhDrD/ETEuwayGVuvqqb36xY9GakGW35R6xvB8Nmk5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46bd505e15bcebe6d7b521ff39cd8be017a8374bdc05a08dd91161895b6a447f","last_reissued_at":"2026-05-18T03:06:20.814149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:20.814149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted norm inequalities for fractional maximal operators--a Bellman function approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.CA","authors_text":"Adam Osekowski, Rodrigo Banuelos","submitted_at":"2013-11-23T17:34:33Z","abstract_excerpt":"We study classical weighted $L^p\\to L^q$ inequalities for the fractional maximal operators on $\\R^d$, proved originally by Muckenhoupt and Wheeden in the 70's. We establish a slightly stronger version of this inequality with the use of a novel extension of Bellman function method.\n  More precisely, the estimate is deduced from the existence of a certain special function which enjoys appropriate majorization and concavity. From this result and an explicit version of the ``$A_{p-\\varepsilon}$ theorem,\" derived also with Bellman functions, we obtain the sharp inequality of Lacey, Moen, P\\'erez an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6025","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1311.6025","created_at":"2026-05-18T03:06:20.814230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.6025v1","created_at":"2026-05-18T03:06:20.814230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6025","created_at":"2026-05-18T03:06:20.814230+00:00"},{"alias_kind":"pith_short_12","alias_value":"I26VAXQVXTV6","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"I26VAXQVXTV6NV5V","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"I26VAXQV","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A","json":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A.json","graph_json":"https://pith.science/api/pith-number/I26VAXQVXTV6NV5VEH7TTTML4A/graph.json","events_json":"https://pith.science/api/pith-number/I26VAXQVXTV6NV5VEH7TTTML4A/events.json","paper":"https://pith.science/paper/I26VAXQV"},"agent_actions":{"view_html":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A","download_json":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A.json","view_paper":"https://pith.science/paper/I26VAXQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.6025&json=true","fetch_graph":"https://pith.science/api/pith-number/I26VAXQVXTV6NV5VEH7TTTML4A/graph.json","fetch_events":"https://pith.science/api/pith-number/I26VAXQVXTV6NV5VEH7TTTML4A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A/action/storage_attestation","attest_author":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A/action/author_attestation","sign_citation":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A/action/citation_signature","submit_replication":"https://pith.science/pith/I26VAXQVXTV6NV5VEH7TTTML4A/action/replication_record"}},"created_at":"2026-05-18T03:06:20.814230+00:00","updated_at":"2026-05-18T03:06:20.814230+00:00"}